Algebra Examples

$\frac{5}{2 x + 3 y} \div \frac{10}{4 x^{2} - 9 y^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2 x + 3 y} \cdot \frac{4 x^{2} - 9 y^{2}}{10}$

Step 2

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1

Factor $5$ out of $10$ .

$\frac{5}{2 x + 3 y} \cdot \frac{4 x^{2} - 9 y^{2}}{5 (2)}$

Step 2.2

Cancel the common factor.

$\frac{5}{2 x + 3 y} \cdot \frac{4 x^{2} - 9 y^{2}}{5 \cdot 2}$

Step 2.3

Rewrite the expression.

$\frac{1}{2 x + 3 y} \cdot \frac{4 x^{2} - 9 y^{2}}{2}$

Step 3

Multiply $\frac{1}{2 x + 3 y}$ by $\frac{4 x^{2} - 9 y^{2}}{2}$ .

$\frac{4 x^{2} - 9 y^{2}}{(2 x + 3 y) \cdot 2}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$\frac{{(2 x)}^{2} - 9 y^{2}}{(2 x + 3 y) \cdot 2}$

Step 4.2

Rewrite $9 y^{2}$ as ${(3 y)}^{2}$ .

$\frac{{(2 x)}^{2} - {(3 y)}^{2}}{(2 x + 3 y) \cdot 2}$

Step 4.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 x$ and $b = 3 y$ .

$\frac{(2 x + 3 y) (2 x - (3 y))}{(2 x + 3 y) \cdot 2}$

Step 4.4

Multiply $3$ by $- 1$ .

$\frac{(2 x + 3 y) (2 x - 3 y)}{(2 x + 3 y) \cdot 2}$

Step 5

Cancel the common factor of $2 x + 3 y$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{(2 x + 3 y) (2 x - 3 y)}{(2 x + 3 y) \cdot 2}$

Step 5.2

Rewrite the expression.

$\frac{2 x - 3 y}{2}$

Step 6

Split the fraction $\frac{2 x - 3 y}{2}$ into two fractions.

$\frac{2 x}{2} + \frac{- 3 y}{2}$

Step 7

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1

Cancel the common factor.

$\frac{2 x}{2} + \frac{- 3 y}{2}$

Step 7.2

Divide $x$ by $1$ .

$x + \frac{- 3 y}{2}$

Step 8

Move the negative in front of the fraction.

$x - \frac{3 y}{2}$